Given an integer n ≥ 2, let X and Y be two generic alternating n × n matrices over a commutative ring k. Denote by k[X, Y ] the polynomial ring with indeterminates the entries of X and Y . Moreover denote by I(XY) the ideal generated by the entries of the product of X and Y . The ring k[X, Y ]/I(XY) is the coordinate ring of the variety of pairs (U, V) of alternating n × n matrices with entries in k, such that UV = 0. In this note we give a k-basis of that coordinate ring, under the assumption that n! is a unit in k. We use some ideas of De Concini, Procesi and Strickland.

On the coordinate ring of pairs of alternating matrices with product zero

DE NEGRI, EMANUELA
2001-01-01

Abstract

Given an integer n ≥ 2, let X and Y be two generic alternating n × n matrices over a commutative ring k. Denote by k[X, Y ] the polynomial ring with indeterminates the entries of X and Y . Moreover denote by I(XY) the ideal generated by the entries of the product of X and Y . The ring k[X, Y ]/I(XY) is the coordinate ring of the variety of pairs (U, V) of alternating n × n matrices with entries in k, such that UV = 0. In this note we give a k-basis of that coordinate ring, under the assumption that n! is a unit in k. We use some ideas of De Concini, Procesi and Strickland.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/212106
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